10/27/2004

Ronny Hadani and Shamgar Gorevitch
Tel Aviv

Proof of the Rudnick-Kurlberg Conjecture

This work is done under the supervision of Professor Joseph Bernstein. Suppose we want to solve some algebraic problem over the fininte field ${\mathbb F}_p$ encoded in a function $\mathrm{F}$. Grothendiek's sheaf-to-function correspondence describes an object (an $l$-adic Weil sheaf) $\mathcal{F}$ from which the function $F$ is derived. The sheaf $\mathcal{F}$ is a geometric object defined over the algebraic closure of ${\mathbb F}_p$. Its properties can be investigated using algebro geometric techniques. In the lecture, we will explain how the above methodology is applied to solve the Rudnick-Kurlberg Conjecture in the theory of quantom chaos.